I think chances are pretty high that you have spelled the first 'wirklich', which means 'in truth', in a different manner than the second one, which means 'to large extent'. At least if you are a German native from the Rhineland-Palatia.

The same can be done if you replace 'wirklich' by 'echt' or 'wahrhaftig'. I believe that English 'really' can be used with two meanings, too, and that both German and English tend to use the same words for both meanings in general. This phenomenon confuses me.

What is the phonetic difference between the two pronunciations? I would even guess it is tonal, but I don't know.

Are these pronunciations variants of the same word, or should they be considered two different words?

No inkling what for you've got the downvote but I fully agree. Wirklich in the first sentence doesn't only sound odd but it is wrong also.
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Em1Jan 1 '13 at 14:15

1

I think it is correct, when you assume that the other person has expressed strong disbelief of the fact of Bob being a Bauer once or twice before the snippet we see here... the intonation would need a strong emphasis on wirklich... long, loud and high pitched... try to ignore the second part of the first sentence and just say "Ich sage dir doch, er ist WIRKLICH ein Bauer."
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EmanuelJan 2 '13 at 12:25

The first wirklich would see a strong emphasis on wirklich probably involving all variables possible (duration, pitch, loudness, gesture).

The second wirklich will have an emphasis too, but it will be matched by an equally stressed Bauer. Without that stress on Bauer it would sound like the first wirklich and that would be confusing as it doesn't make sense.

Note that there is one specific emphasis that does apply in neither of the examples... a strong pitch raise between wirk and lich. That would sound (to me) like the meaning Hubert suggested in his answer and as such it is weird but not unheard of.

Is it one word? My first reaction was "of course" but then what do you do with "ihr"... is that one word or 3... to me it is 3 so why should wirklich be only 1. But then again if we go down this route, anstellen would be at least 5 words and I don't know if we want to do that... so I guess eventually it is a question of your personal perspective. To me both meanings are similar enough in core and grammar that it counts as one. Ihr has 3 totally different meanings with different grammar, hence 3... but that is just my opinion.